"Find the sum of the x-coordinates of the solutions to the system of equations y=|x^2-6x+5| and y=(29/4)-x."
I tried to solve it by using casework & factoring, but that quickly lead to a dead-ish end.
too bad you didn't bother to show your work ...
the absolute value means you have to solve two problems:
x^2-6x+5 >= 0 (that is, x <= 1 or x >= 5
x^2-6x+5 = 29/4 -x
x = (5±√17)/2 = 0.438 or 4.56
only x = (5-√17)/2 fits the initial criteria
or
x^2-6x+5 < 0 (that is 1<x<5)
x^2-6x+5 = x - 29/4
x = 7/2
so the sum of the solutions is
6-√17/2